Lewis Hyde devotes 10 pages of The Gift to Warren O. Hagstrom’s interpretation of science as a “gift community; in other words, a community in which “knowledge circulates freely.” Hagstrom is a sociologist of science; he wrote a few papers about the sociology of mathematics, which I quote in Chapter 2, but I didn’t quote his 1965 book The Scientific Community, possibly because it includes sentences like this one (p. 189; Basic Books):
Mathematics derives its prestige largely from its being the servant of the sciences; it contributes to them all, but they make no real contributions to it in return…
Hagstrom’s analysis of scientific research, on Hyde’s account, applies word for word to mathematics. “Manuscripts submitted to scientific periodicals are often called ‘contributions,’ and they are, in fact, gifts.” We don’t get paid for our papers; we may get paid for writing textbooks, but this “tends to be a despised form of scientific communication” because “the textbook author appropriates community property for his personal profit.”
(Let me pause to reassure the reader that the profit I have obtained by “appropriating” my professional milieu for the purposes of Mathematics without Apologies has been exceedingly modest!)
Hyde then turns to the Kwakiutl of the Northwest coast to answer the question: can’t our “contributions,” for which we are not paid, be better seen “in terms of ambition and egotism” in our competition for status within the community?
[W]e shoudl notice that the kind of status we are speaking of is achieved through donation, not through acquisition.… Kwakiutl names … are not the names of individuals; they are conferred upon individuals … but they are… meant to indicate social position.
The Kwakiutl names include “Whose Property is Eatin in Feasts,” “Always Giving Blankets While Walking,” “The Dance of Throwing Away Property.”
A scientist does contribute his ideas in order to earn status, but if the name he makes for himself is He Whose Ideas Are Eaten in Conferences, we need not call his contributions meretricious.
Hyde goes on to speculate on why scientific ideas are treated as gifts. He notes, for example, that the ideas must fit into the scientific community’s shared framework, and suggests that this community arises from the exchange of gifts in the form of ideas. There is competition, of course, but he sees this as a phenomenon built on the non-commercial foundations of the gift.
[A]s long as the goals of science require an intellectual community congenial to discourse and capable of integrating a coherent body of theory, gift exchange will be a part of its commerce.
So competing for high salaries and prestigious jobs — which is not unknown even in mathematics! — is only possible because the community is sustained by the practice of sharing rather than on the free market.
All of the quotations are from the (second) 2007 Vintage edition of Hyde’s book, which is subtitled Creativity and the Artist in the Modern World. The original subtitle was Imagination and the Erotic Life of Property; he doesn’t explain why he changed it, and I’m sorry he did. On the other hand, in the preface to the second edition he says he wouldn’t mind if Vintage pitched the book as “Bad-boy critic takes on vampire economy” — which, come to think of it, isn’t a bad pitch for my book! In the introduction he writes that, in a market society,
[A] disquieting sense of triviality, of worthlessness even, will nag the man or woman who labors in the service of a gift and whose products are not adequately described as commodities.
Exactly! It’s exactly this sense of worthlessness that compels us to attempt to justify mathematics as a means to some end recognized by the market.
Although I still think I was right to argue in Chapter 2 that value in mathematics is (tautologically) inseparable from hierarchy, I regret that I didn’t devote more time to the vision of mathematics as a community built on cooperation. I would undoubtedly have done so if I had read Hyde’s book. Most of the book is about seeing art (literature, poetry) as a gift. I’m still waiting for the part where he explains how the artist (or the poet, or the mathematician) is supposed to get the external goods necessary for material survival; but I’m beginning to suspect he doesn’t have an answer.